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Existence of positive solutions for a class of delay fractional differential equations with generalization to N-term. (English) Zbl 1217.34007
Summary: We established the existence of a positive solution of nonlinear fractional differential equations 𝔏(D)[x(t)-x(0)]=f(t,x t ),t(0,b] with finite delay x(t)=ω(t),t[-τ,0], where lim t0 f(t,x t )=+, that is, f is singular at t=0 and x t C([-τ,0], 0 . The operator of 𝔏(D) involves the Riemann-Liouville fractional derivatives. In this problem, the initial conditions with fractional order and some relations among them were considered. The analysis rely on the alternative of the Leray-Schauder fixed point theorem, the Banach fixed point theorem, and the Arzela-Ascoli theorem in a cone.
MSC:
34A08Fractional differential equations